Density Functional Theory (DFT) calculations were used to determine physical properties of bulk GaN and GaN(0001), i.e. N-terminated surface. The bulk data are in agreement with the theoretical and experimental data reported by Magnuson et al. [M. Magnuson et al., Phys. Rev. B 81 (2010) 085125], demonstrating that bonding in GaN is of a mixed nature in which Ga 4s, Ga 4p, Ga 3d, and N 2s, N 2p orbitals are involved. Ga 4s and Ga 4p states are sp3 hybridized while the N states are involved independently in bonding. Ga sp3 states overlap with the N 2s states creating the upper subband extending down to 6 eV below the valence band maximum (VBM). The lower valence band (VB) subband is composed of Ga 3d states overlapping with N 2s states whose energy levels range from 13 to 17 eV below VBM. GaN bulk bonding enforces creation of the two surface states at clean GaN(0001) surface: the lower energy state, located 15 eV below VBM is composed of N 2s states. The upper energy surface state, located below VBM, is composed of N 2pz nonsaturated state, i.e. it is of the broken bond type. The Fermi energy is pinned by this dispersionless acceptor state. Ga adsorption leads to emergence of donor state, which pins the Fermi level at 1.1 eV above VBM which is compatible with the Fermi level pinned at the surface for p-type GaN and is inconsistent with n-type bulk. The total energy of slab has the energy lower by about 2 eV for the adsorbed than for the separate Ga atom. The inconsistent data obtained from thermodynamic stability and band diagram analyses suggest further investigations to explain inconsistencies between these two pictures.